This invention relates to digital communications, and more particularly to determining the combination of transmitted pulse shape and receiver sampling time that optimizes the magnitude of the digital channel output pulse sample.
As is well known, in amplitude-shift-keying (ASK) digital communications pulses are transmitted by a transmitter to a receiver, which then samples the received signal in each pulse time interval to determine what magnitude was actually sent by the transmitter. Generally, in each pulse time interval the same pulse shape is transmitted with different discrete amplitudes, each possible amplitude representing either a single bit or plural binary bits. For example, in each interval the maximum amplitude of the pulse can either be zero or a fixed value, A, in which case each pulse represents a binary "0" or "1". Alternatively, the maximum pulse value in an interval, A.sub.m, can assume plural level values, in which case each level can represent more than one binary bit. Because of the various impairments such as noise that affect the transmission of pulses through a channel, the received pulse in each pulse time interval does not exactly duplicate the transmitted pulse in either shape or maximum magnitude. The receiver, in order to recover the underlying binary bit or bits that each pulse represents, samples the received pulse at some sampling instant within each pulse interval and from that sampled magnitude makes a decision as to what pulse magnitude was most likely transmitted. In the prior art, in order to provide greatest immunity to noise, the transmitted pulses are shaped to deliver the maximum energy to the receiver and are then sampled at the time at which the received pulse is a maximum. In the past, however, in order to suppress noise, channel bandwidth has generally been kept at the Nyquist bandwidth. When transmitting at this minimum bandwidth, the optimal pulse shape is controlled since there is only one pulse shape that transmits most of its energy through the minimum bandwidth channel, that pulse shape being the prolate spheroidal wave function. Non-optimal waveforms that are easy to generate and hence have been used in practical applications lose much of their energy when transmitted through the channel. These waveforms, therefore, are more susceptible to noise than the optimal pulse shape.
Recently it has been recognized that when the noise is colored rather than white, advantages may accrue in using a channel having a bandwidth greater than the Nyquist bandwidth. Specifically, with a wider bandwidth channel the correlation in the noise can be exploited to reduce noise in the receiver. With a wider bandwidth channel the flexibility exists for shaping the pulses for various purposes. These purposes include shaping a pulse to minimize loss through the channel, and shaping a pulse to maximize the output pulse value at a given time instant. Obviously, with a maximized pulse value at the sampling time, there will be a maximum signal-to-noise ratio and generally improved immunity to interference of various kinds.
Various approaches to pulse shaping for improved signal-to-noise performance have been taken in the prior art. These approaches either look for a pulse that has a local maximum at the sampling instant (see, e.g., Transmission Systems for Communications, Fifth Edition, Members of the Technical Staff Bell Telephone Laboratories, 1982, pp. 714-728), or alternatively, given a fixed sampling instant, select a "best" pulse for that sampling instant (see, e.g., J. Lechleider, "A New Interpolation Theorem with Application to Pulse Transmission", IEEE Transactions on Communications, Vol. 39, No. 10, Oct. 1991, pp. 1438-1444). The prior art, however, has not addressed the joint optimization of pulse shape and receiver sampling time that maximizes the magnitude of the channel output pulse sample.